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1. Field of the Invention
The present invention relates generally to a method for reconstructing images of vascular structures and more specifically to an improved method for three-dimensional (3-D) reconstruction of vascular structures from two two-dimensional biplane projection images and methods and structures for quantitative analysis of such a reconstructed structure.
2. Discussion of Related Art
Several investigators have reported computer assisted methods for estimation of the 3-D coronary arteries from biplane projection data. These known methods are based on the known or standard X-ray geometry of the projections, placement of landmarks, known vessel shape, and on iterative identification of matching structures in two or more views. Such methods are described in a publication entitled xe2x80x9c3-D digital subtraction angiographyxe2x80x9d, IEEE Trans. Med. Imag., vol. MI-1, pp. 152-158, 1982 by H. C. Kim, B. G. Min, T. S. Lee, et. al. and in a publication entitled xe2x80x9cMethods for evaluating cardiac wall motion in 3-D using bifurcation points of the coronary arterial treexe2x80x9d, Invest. Radiology, January-February pp. 47-56, 1983 by M. J. Potel, J. M. Rubin, and S. A. Mackay, et al. Because the computation was designed for predefined views only, it is not suitable to solve the reconstruction problem on the basis of two projection images acquired at arbitrary and unknown relative orientations.
Another known method is based on motion and multiple views acquired in a single-plane imaging system. Such a method is described in a publication entitled xe2x80x9cReconstructing the 3-d medial axes of coronary arteries in single-view cineangiogramsxe2x80x9d, IEEE Trans. MI, vol. 13, no. 1, pp. 48-60, 1994 by T. V. Nguyen and J. Sklansky uses motion transformations of the heart model. However, the motion transformations of the heart model consist only of rotation and scaling. By incorporation of the center-referenced method, initial depth coordinates, and center coordinates, a 3-D skeleton of the coronary arteries was obtained. However, the real heart motion during the contraction involves five specific movements: translation, rotation, wringing, accordion-like motion, and movement toward the center of the ventricular chamber. Therefore, the model employed is not general enough to portray the true motion of the heart, especially toward the end-systole.
Knowledge-based or rule-based systems have been proposed for 3-D reconstruction of coronary arteries by use of a vascular network model. One such knowledge-based system is described in a publication entitled xe2x80x9cAn expert system for the labeling and 3-D reconstruction of the coronary arteries from two projectionsxe2x80x9d, International Journal of Imaging, Vol. 5, No. 2-3, pp. 145-154, 1990 by Smets, Vandewerf, Suctens, and Oosterlinck. Because the rules or knowledge base were organized for certain specific conditions, it does not generalize the 3-D reconstruction process to arbitrary projection data. In other knowledge-based systems, the 3-D coronary arteries were reconstructed from a set of X-ray perspective projections by use of an algorithm from computed tomography. Due to the motion of the heart and only a limited number of projections (four or six), accurate reconstruction and quantitative measurement are not easily achieved.
Closed-form solutions of the 3-D reconstruction problem using a linear approach was a significant development and is described in, for example, a publication entitled xe2x80x9cDetermining 3-d motion and structure of a rigid body using the spherical projectionxe2x80x9d, CVGIP, vol. 21, pp. 21-32, 1983 by B. L. Yen and T. S. Huang. Unfortunately, actual data is always corrupted by noise or errors and the linear approach based techniques may not be sufficiently accurate when using noisy data. Hence, optimal estimation has been explicitly investigated. Additionally, U.S. Pat. No. 4,875,165 entitled Method for Determination of 3-D Structures in Biplane Angiography issued in the name of Fencil et al. also has significant drawbacks.
Use of a two-step method is known for producing an optimal estimation for a 3-D structure based on maximum-likelihood and minimum-variance estimation. In these techniques, for example, two publications entitled xe2x80x9cOptimal motion and structure estimationxe2x80x9d, IEEE Trans. on PAMI, Vol. 15, no. 9, September 1993, pp. 864-884, and xe2x80x9cStructure from motion using the reconstruction and projection techniquexe2x80x9d, Proc. IEEE Workshop Computer Vision, November 1987, pp. 345-348, image error was employed in the objective function for a non-constricted minimization process. Preliminary estimates computed by a linear algorithm were used as initial estimates for the process of optimal estimation. However, if the initial solution from the linear approach is not sufficient, (e.g., with more than 2 pixels=0.6 mm error in the input 2-D image data), the iterative minimization process at the second step may become trapped in a local minimum due to a lack of prior information concerning the variables to be optimized.
Quantitative coronary analysis (xe2x80x9cQCAxe2x80x9d) of a reconstruction of an arterial tree was known and developed in the 1970""s to quantify vessel geometry and the effects of drugs on the regression and progression of coronary artery disease. In the mid-1980""s, digital systems were introduced into the catheterization laboratory to support the angiographer during the interventional procedures. With the advent digital angiographic technology, on-line QCA has been widely used predominantly for the selection of the optimal sizes of the interventional devices, and for the assessment of the efficacy of the procedure. However, current QCA techniques are performed on the 2-D projection views in which the vessel overlap and foreshortening are subjectively minimized in a xe2x80x9ctrial-and-errorxe2x80x9d manner by the interventionist. FIGS. 56(a)-(d) demonstrate the problems resulting from use of such 2-D projections in QCA techniques. FIG. 56c is an RCA image as known in the art used for QCA and resulting in a 30% narrowing measurement as shown in FIG. 56d. With 2-D projection views there is no way to know or estimate how much error occurs in the QCA process due to foreshortening with respect to the stentotic segment. In FIGS. 56a and 56b, the same vessel segment between two bifurcation points as marked by two dots at its proximal and distal ends depicts 77% and 52% foreshortening, respectively.
It is evident from the above discussion that a need exists for improved reconstruction of 3-D images from 2-D image data and that a further need exists for improved QCA techniques utilizing such 3-D reconstruction to provide needed analysis in the intervention process.
The disadvantages of present methods known for visual reconstruction of vascular structures are substantially overcome with the present invention by providing a novel method for three-dimensional reconstruction of vessels using two-dimensional angiograms and further by providing improved QCA techniques utilizing such 3-D reconstructions of vascular structures.
This patent application teaches the methods and structures of the invention with reference to vascular structures (i.e., coronary arteries or coronary arterial trees). Those skilled in the art will readily recognize that the improved reconstruction methods and the quantitative analysis methods and structures are equally applicable to any vascular structure. References herein to xe2x80x9ccoronaryxe2x80x9d or xe2x80x9carterialxe2x80x9d applications of the invention are intended merely as exemplary of common vascular structures where such reconstruction and analysis techniques are beneficially applied. Nothing in this patent application should be construed as limiting the reconstruction and analysis features to coronary applications. In particular, reference to xe2x80x9cquantitative coronary analysisxe2x80x9d (or xe2x80x9cQCAxe2x80x9d) should be understood to refer broadly to quantitative analysis of any vascular structures. Likewise, reference to an xe2x80x9carteryxe2x80x9d or xe2x80x9carteriesxe2x80x9d should be broadly understood to refer to any vessel or vessels. xe2x80x9cArtery treexe2x80x9d, xe2x80x9carterial treexe2x80x9d, xe2x80x9ccoronary arterial treexe2x80x9d or xe2x80x9ccoronary artery treexe2x80x9d should all be understood to broadly refer to any vascular tree structure. Coronary applications of the present invention are therefore merely one common exemplary application of the features, methods and structures of the present invention.
In the present inventive method, a novel optimization technique minimizes the image point errors and directional vector errors in both imaging systems subject to the constraints derived from the individual intrinsic imaging parameters of the employed imaging system. Given five or more corresponding object points in both views (projection image), a constrained nonlinear optimization algorithm is applied to obtain an optimal estimate (transformation) of the biplane imaging geometry in the form of R and {right arrow over (t)} which characterize the position and orientation of one imaging system (imaging portion of the imaging system) relative to the other. The initial solution is estimated on the basis of the individual intrinsic imaging parameters.
Angiograms of eight hundred patients were analyzed in which two cases are selected for discussion hereinafter. The biplane imaging geometry was first determined without a calibration object, and the 3-D coronary arterial trees were reconstructed, including both left and right coronary artery systems. Various two-dimensional (2-D) projection images of the reconstructed 3-D coronary arterial tree were generated and compared to other viewing angles obtained in the actual patient study. Similarity between the real and reconstructed arterial structures was excellent. The accuracy of this method was evaluated by using a computer-simulated coronary arterial tree. Root-mean-square (RMS) errors in the 3-D position and the 3-D configuration of vessel centerlines and in the angles defining the R matrix and {right arrow over (t)} vector were 0.9-5.5 mm, 0.7-1.0 mm, and less than 1.5 and 2.0 degrees, respectively, when using 2-D vessel centerlines with RMS normally distributed errors varying from 0.4-4.2 pixels (0.25-1.26 mm).
More specifically, the method for three-dimensional reconstruction of a target object from two-dimensional images involves a target object having a plurality of branch-like vessels. The method includes the steps of: a) placing the target object in a position to be scanned by an imaging system, the imaging system having a plurality of imaging portions; b) acquiring a plurality of projection images of the target object, each imaging portion providing a projection image of the target object, each imaging portion disposed at an unknown orientation relative to the other imaging portions; c) identifying two-dimensional vessel centerlines for a predetermined number of the vessels in each of the projection images; d) creating a vessel hierarchy data structure for each projection image, the data structure including the identified two-dimensional vessel centerlines defined by a plurality of data points in the vessel hierarchy data structure; e) calculating a predetermined number of bifurcation points for each projection image by traversing the corresponding vessel hierarchy data structure, the bifurcation points defined by intersections of the two-dimensional vessel centerlines; f) determining a transformation in the form of a rotation matrix and a translation vector utilizing the bifurcation points corresponding to each of the projections images, the rotation matrix, and the translation vector representing imaging parameters corresponding to the relative orientations of the imaging portions of the imaging system; g) utilizing the data points and the transformation to establish a correspondence between the two-dimensional vessel centerlines corresponding to each of the projection images such that each data point corresponding to one projection image is linked to a data point corresponding to the other projection images, the linked data points representing an identical location in the vessel of the target object after the projections; h) calculating three-dimensional vessel centerlines utilizing the two-dimensional vessel centerlines and the correspondence between the data points of the two-dimensional vessel centerlines; and i) reconstructing a three-dimensional visual representation of the target object based on the three-dimensional vessel centerlines and diameters of each vessel estimated along the three-dimensional centerline of each vessel; and j) determining the optimal view of the vessel segments with minimal vessel foreshortening.
Further features of the present invention utilize such 3-D reconstructions to provide improved QCA techniques for analysis of coronary artery images.